Preheat your oven to 350°F (177°C) and line a 12-count muffin pan with cupcake liners. Line an additional pan with two liners, as this recipe yields about 14 cupcakes. Set aside.
In a bowl, whisk together the cake flour, baking powder, baking soda, and salt. Set this dry mixture aside.
Using a handheld or stand mixer fitted with a paddle attachment, beat the butter on high speed for about 1 minute until smooth and creamy. Add the sugar and continue beating on high for 2 minutes until light and fluffy, scraping down the sides and bottom of the bowl with a silicone spatula as needed.
Add the egg whites, vanilla extract, and peppermint extract, and beat on medium-high speed until fully combined. Then add the sour cream and mix again, scraping the bowl as needed.
With the mixer on low speed, gradually add the dry ingredients until just combined. Keeping the mixer on low, slowly pour in the milk and mix until incorporated. Avoid over-mixing—whisk gently by hand if necessary to ensure no lumps remain. The batter will be slightly thick.
Spoon the batter into the cupcake liners, filling each about two-thirds full to prevent overflow during baking. Bake for 19 to 22 minutes, or until a toothpick inserted into the center comes out clean. For about 30 mini cupcakes, bake for 11 to 13 minutes at the same temperature. Allow the cupcakes to cool completely before frosting.
While the cupcakes cool, melt the white chocolate for the frosting. Place the chopped chocolate in a microwave-safe bowl and heat in 20-second intervals, stirring after each, until smooth. Let it cool at room temperature for 20 minutes so it is melted but not too hot to avoid melting the butter later.
To make the frosting, beat the butter in a medium bowl using a handheld or stand mixer with a paddle attachment on medium speed for 1 minute. Reduce the speed to low and gradually add the confectioners’ sugar. Stir the cooled white chocolate until smooth, then add it to the butter and sugar mixture. Increase the mixer speed to medium and beat for 2 minutes until well combined and creamy.
Add the heavy cream, vanilla extract, peppermint extract, and salt, then beat for 1 minute until fully blended. Taste and adjust by adding an extra tablespoon of heavy cream or milk if you prefer a thinner consistency, or add a pinch more salt if the frosting tastes too sweet.
Frost the cooled cupcakes. For a decorative touch, see the note about swirled frosting. Top with crushed candy canes and coarse sugar sprinkles if desired.
Store any leftovers in the refrigerator for 3 to 4 days.